diff --git a/lib/matplotlib/backends/backend_mixed.py b/lib/matplotlib/backends/backend_mixed.py
index 36c0896f3097..187d08aab27c 100644
--- a/lib/matplotlib/backends/backend_mixed.py
+++ b/lib/matplotlib/backends/backend_mixed.py
@@ -86,6 +86,18 @@ def start_rasterizing(self):
                                                self._raster_renderer)
             self._bbox_inches_restore = r
 
+    def get_image_magnification(self):
+        """
+        Return the magnification factor for rasterized content.
+
+        When using `.MixedModeRenderer`, the figure DPI is set to the vector
+        renderer's DPI (typically 72 for PDF/SVG/PS) but rasterized content
+        is drawn at ``self.dpi`` (the user's requested DPI). This factor
+        converts from vector-space display coordinates to raster-space pixel
+        coordinates.
+        """
+        return self.dpi / self._figdpi
+
     def stop_rasterizing(self):
         """
         Exit "raster" mode.  All of the drawing that was done since
diff --git a/lib/matplotlib/offsetbox.py b/lib/matplotlib/offsetbox.py
index 9b9c7a69f35f..cb8fc7e21991 100644
--- a/lib/matplotlib/offsetbox.py
+++ b/lib/matplotlib/offsetbox.py
@@ -37,6 +37,7 @@
 from matplotlib.patches import (
     FancyBboxPatch, FancyArrowPatch, bbox_artist as mbbox_artist)
 from matplotlib.transforms import Bbox, BboxBase, TransformedBbox
+from matplotlib.backends.backend_mixed import MixedModeRenderer
 
 
 DEBUG = False
@@ -689,9 +690,6 @@ def draw(self, renderer):
         self.dpi_transform.clear()
         self.dpi_transform.scale(dpi_cor)
 
-        # At this point the DrawingArea has a transform
-        # to the display space so the path created is
-        # good for clipping children
         tpath = mtransforms.TransformedPath(
             mpath.Path([[0, 0], [0, self.height],
                         [self.width, self.height],
@@ -700,7 +698,28 @@ def draw(self, renderer):
         for c in self._children:
             if self._clip_children and not (c.clipbox or c._clippath):
                 c.set_clip_path(tpath)
-            c.draw(renderer)
+            if c.get_rasterized() and isinstance(renderer, MixedModeRenderer):
+                # When using MixedModeRenderer (PDF/SVG/PS), the figure DPI is
+                # set to the vector renderer's DPI (typically 72 pt/inch), so
+                # dpi_cor ≈ 1.0. But rasterized children are drawn into a
+                # RendererAgg buffer at renderer.dpi (the user's requested DPI).
+                # The child's transform is dpi_transform + offset_transform,
+                # where offset_transform is a translation in vector-DPI display
+                # units. Both must be scaled to raster-DPI pixel coordinates.
+                mag = renderer.get_image_magnification()
+                raster_dpi_cor = dpi_cor * mag
+                off_mat = self.offset_transform.get_matrix().copy()
+                scaled_off = off_mat.copy()
+                scaled_off[:2, 2] *= mag  # scale tx and ty to raster DPI
+                self.dpi_transform.clear()
+                self.dpi_transform.scale(raster_dpi_cor)
+                self.offset_transform.set_matrix(scaled_off)
+                c.draw(renderer)
+                self.dpi_transform.clear()
+                self.dpi_transform.scale(dpi_cor)
+                self.offset_transform.set_matrix(off_mat)
+            else:
+                c.draw(renderer)
 
         _bbox_artist(self, renderer, fill=False, props=dict(pad=0.))
         self.stale = False
@@ -899,7 +918,26 @@ def get_bbox(self, renderer):
     def draw(self, renderer):
         # docstring inherited
         for c in self._children:
-            c.draw(renderer)
+            if c.get_rasterized() and isinstance(renderer, MixedModeRenderer):
+                # offset_transform and ref_offset_transform store display-unit
+                # translations computed at vector DPI (typically 72 pt/inch for
+                # PDF/SVG/PS). When rasterizing, the RendererAgg buffer uses
+                # renderer.dpi (user DPI). Scale the translation components so
+                # the child draws at the correct position in the raster buffer.
+                mag = renderer.get_image_magnification()
+                off_mat = self.offset_transform.get_matrix().copy()
+                ref_mat = self.ref_offset_transform.get_matrix().copy()
+                scaled_off = off_mat.copy()
+                scaled_off[:2, 2] *= mag  # scale tx and ty only
+                scaled_ref = ref_mat.copy()
+                scaled_ref[:2, 2] *= mag
+                self.offset_transform.set_matrix(scaled_off)
+                self.ref_offset_transform.set_matrix(scaled_ref)
+                c.draw(renderer)
+                self.offset_transform.set_matrix(off_mat)
+                self.ref_offset_transform.set_matrix(ref_mat)
+            else:
+                c.draw(renderer)
         _bbox_artist(self, renderer, fill=False, props=dict(pad=0.))
         self.stale = False
 
diff --git a/lib/matplotlib/tests/test_offsetbox.py b/lib/matplotlib/tests/test_offsetbox.py
index f126b1cbb466..cae8a4988bfd 100644
--- a/lib/matplotlib/tests/test_offsetbox.py
+++ b/lib/matplotlib/tests/test_offsetbox.py
@@ -12,8 +12,9 @@
 from matplotlib.backend_bases import MouseButton, MouseEvent
 
 from matplotlib.offsetbox import (
-    AnchoredOffsetbox, AnnotationBbox, AnchoredText, DrawingArea, HPacker,
-    OffsetBox, OffsetImage, PaddedBox, TextArea, VPacker, _get_packed_offsets)
+    AnchoredOffsetbox, AnnotationBbox, AnchoredText, AuxTransformBox,
+    DrawingArea, HPacker, OffsetBox, OffsetImage, PaddedBox, TextArea, VPacker,
+    _get_packed_offsets)
 
 
 @image_comparison(['offsetbox_clipping'], remove_text=True)
@@ -507,3 +508,49 @@ def test_anchored_offsetbox_tuple_and_float_borderpad():
     # in the y-direction.
     assert pos_tuple_asym.x0 > pos_float.x0
     assert pos_tuple_asym.y0 < pos_float.y0
+
+
+@check_figures_equal(extensions=["pdf", "svg", "png"], tol=5)
+def test_rasterized_artist_in_drawing_area(fig_test, fig_ref):
+    """Rasterized artists in DrawingArea must be correctly positioned in
+    vector backends. Regression test for
+    https://github.com/matplotlib/matplotlib/issues/28549
+    """
+    from matplotlib.collections import PatchCollection
+    from matplotlib.patches import Rectangle
+
+    def make_plot(fig, rasterized):
+        ax = fig.subplots()
+        box = DrawingArea(10, 10)
+        rects = PatchCollection(
+            [Rectangle((0, i), width=10, height=1) for i in range(10)]
+        )
+        rects.set_rasterized(rasterized)
+        box.add_artist(rects)
+        ax.add_artist(AnchoredOffsetbox(child=box, loc="center", pad=0))
+
+    make_plot(fig_test, rasterized=True)
+    make_plot(fig_ref, rasterized=False)
+
+
+@check_figures_equal(extensions=["pdf", "svg", "png"], tol=8)
+def test_rasterized_artist_in_aux_transform_box(fig_test, fig_ref):
+    """Rasterized artists in AuxTransformBox must be correctly positioned in
+    vector backends. Regression test for
+    https://github.com/matplotlib/matplotlib/issues/28549
+    """
+    from matplotlib.patches import Ellipse
+
+    def make_plot(fig, rasterized):
+        ax = fig.subplots()
+        ax.set_xlim(0, 10)
+        ax.set_ylim(0, 10)
+        # Use ax.transData as the typical real-world use of AuxTransformBox
+        box = AuxTransformBox(ax.transData)
+        el = Ellipse((5, 5), width=4, height=2)
+        el.set_rasterized(rasterized)
+        box.add_artist(el)
+        ax.add_artist(AnchoredOffsetbox(child=box, loc="center", pad=0))
+
+    make_plot(fig_test, rasterized=True)
+    make_plot(fig_ref, rasterized=False)